2021/02/12 by Chakraborty, Himadri Shekhar, Miezaki, Tsuyoshi · 1 citation
#11F11 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Primary: 11T71 #Secondary: 94B05
paper · doi:10.48550/arxiv.2102.06369
In this paper, we introduce the notion of the complete joint Jacobi polynomial of two linear codes of length n over \mathbbFq and ℤk. We give the MacWilliams type identity for the complete joint Jacobi polynomials of codes. We also introduce the concepts of the average Jacobi polynomial and the average complete joint Jacobi polynomial over \mathbbFq and ℤk. We give a representation of the average of the complete joint Jacobi polynomials of two linear codes of length n over \mathbbFq and ℤk in terms of the compositions of n and its distribution in the codes. Further we present a generalization of the representation for the average of the (g+1)-fold complete joint Jacobi polynomials of codes over \mathbbFq and ℤk. Finally, we give the notion of the average Jacobi intersection number of two codes.